# Local and global $\Lambda$ polarization in a vortical fluid

## TL;DR

This paper calculates the fermion spin distribution in a vortical fluid created in heavy-ion collisions, linking local vorticity to spin polarization and comparing global polarization results with experimental data.

## Contribution

It introduces a detailed event-by-event (3+1)D viscous hydrodynamic model to study local and global fermion polarization in vortical fluids.

## Key findings

- Local vorticity correlates with fermion spin distribution.
- Global polarization results match STAR experimental data.
- Energy dependence of polarization is consistent with observations.

## Abstract

We compute the fermion spin distribution in the vortical fluid created in off-central high-energy heavy-ion collisions. We employ the event-by-event (3+1)D viscous hydrodynamic model. The spin polarization density is proportional to the local fluid vorticity in quantum kinetic theory. As a result of strong collectivity, the spatial distribution of the local vorticity on the freeze-out hyper-surface strongly correlates to the rapidity and azimuthal angle distribution of fermion spins. We investigate the sensitivity of the local polarization to the initial fluid velocity in the hydrodynamic model and compute the global polarization of {\Lambda} hyperons by the AMPT model. The energy dependence of the global polarization agrees with the STAR data.